Editing Bell number (section)

==Triangle scheme for calculations==
{{main article|Bell triangle}}
[[Image:BellNumberAnimated.gif|right|thumb|The triangular array whose right-hand diagonal sequence consists of Bell numbers]]
The Bell numbers can easily be calculated by creating the so-called [[Bell triangle]], also called '''Aitken's array''' or the '''Peirce triangle''' after [[Alexander Aitken]] and [[Charles Sanders Peirce]].<ref>{{Cite OEIS|A011971|name=Aitken's array}}</ref>

# Start with the number one.  Put this on a row by itself. (<math> x_{0,1} = 1 </math>)
# Start a new row with the rightmost element from the previous row as the leftmost number (<math>x_{i,1} \leftarrow x_{i-1, r}</math> where ''r'' is the last element of (''i''-1)-th row)
# Determine the numbers not on the left column by taking the sum of the number to the left and the number above the number to the left, that is, the number diagonally up and left of the number we are calculating <math>( x_{i,j} \leftarrow x_{i,j-1} + x_{i-1,j-1} )</math> 
# Repeat step three until there is a new row with one more number than the previous row (do step 3 until <math> j = r + 1 </math>)
# The number on the left hand side of a given row is the ''Bell number'' for that row. (<math>B_i \leftarrow x_{i,1}</math>)

Here are the first five rows of the triangle constructed by these rules:

<math>
\begin{array}{l}
  1 \\
  1 &  2 \\
  2 &  3 &  5 \\
  5 &  7 & 10 & 15 \\
 15 &  20 &  27 &  37 & 52
\end{array}
</math>

The Bell numbers appear on both the left and right sides of the triangle.